Chargement des librairies

library(corrplot)
## corrplot 0.92 loaded
library(cluster)
library(NbClust)

1 - Compréhension et pré-traitement des données

donnee <- read.csv("Pays_donnees.csv", sep = ',', row.names = 1)
head(donnee,5)
##                     enfant_mort exports sant. imports revenu inflation
## Afghanistan                90.2    10.0  7.58    44.9   1610      9.44
## Albania                    16.6    28.0  6.55    48.6   9930      4.49
## Algeria                    27.3    38.4  4.17    31.4  12900     16.10
## Angola                    119.0    62.3  2.85    42.9   5900     22.40
## Antigua and Barbuda        10.3    45.5  6.03    58.9  19100      1.44
##                     esper_vie fert pib_h
## Afghanistan              56.2 5.82   553
## Albania                  76.3 1.65  4090
## Algeria                  76.5 2.89  4460
## Angola                   60.1 6.16  3530
## Antigua and Barbuda      76.8 2.13 12200
str(donnee)
## 'data.frame':    167 obs. of  9 variables:
##  $ enfant_mort: num  90.2 16.6 27.3 119 10.3 14.5 18.1 4.8 4.3 39.2 ...
##  $ exports    : num  10 28 38.4 62.3 45.5 18.9 20.8 19.8 51.3 54.3 ...
##  $ sant.      : num  7.58 6.55 4.17 2.85 6.03 8.1 4.4 8.73 11 5.88 ...
##  $ imports    : num  44.9 48.6 31.4 42.9 58.9 16 45.3 20.9 47.8 20.7 ...
##  $ revenu     : int  1610 9930 12900 5900 19100 18700 6700 41400 43200 16000 ...
##  $ inflation  : num  9.44 4.49 16.1 22.4 1.44 20.9 7.77 1.16 0.873 13.8 ...
##  $ esper_vie  : num  56.2 76.3 76.5 60.1 76.8 75.8 73.3 82 80.5 69.1 ...
##  $ fert       : num  5.82 1.65 2.89 6.16 2.13 2.37 1.69 1.93 1.44 1.92 ...
##  $ pib_h      : int  553 4090 4460 3530 12200 10300 3220 51900 46900 5840 ...
dim(donnee)
## [1] 167   9

Nous avons 167 individus et 9 variables

Statistiques descriptives

summary(donnee)
##   enfant_mort        exports            sant.           imports        
##  Min.   :  2.60   Min.   :  0.109   Min.   : 1.810   Min.   :  0.0659  
##  1st Qu.:  8.25   1st Qu.: 23.800   1st Qu.: 4.920   1st Qu.: 30.2000  
##  Median : 19.30   Median : 35.000   Median : 6.320   Median : 43.3000  
##  Mean   : 38.27   Mean   : 41.109   Mean   : 6.816   Mean   : 46.8902  
##  3rd Qu.: 62.10   3rd Qu.: 51.350   3rd Qu.: 8.600   3rd Qu.: 58.7500  
##  Max.   :208.00   Max.   :200.000   Max.   :17.900   Max.   :174.0000  
##      revenu         inflation         esper_vie          fert      
##  Min.   :   609   Min.   : -4.210   Min.   :32.10   Min.   :1.150  
##  1st Qu.:  3355   1st Qu.:  1.810   1st Qu.:65.30   1st Qu.:1.795  
##  Median :  9960   Median :  5.390   Median :73.10   Median :2.410  
##  Mean   : 17145   Mean   :  7.782   Mean   :70.56   Mean   :2.948  
##  3rd Qu.: 22800   3rd Qu.: 10.750   3rd Qu.:76.80   3rd Qu.:3.880  
##  Max.   :125000   Max.   :104.000   Max.   :82.80   Max.   :7.490  
##      pib_h       
##  Min.   :   231  
##  1st Qu.:  1330  
##  Median :  4660  
##  Mean   : 12964  
##  3rd Qu.: 14050  
##  Max.   :105000
# Histogramme de chaque variable
par(mfrow=c(3,3)) # Afficher les 9 histogrammes dans une grille 3x3
for (i in 1:9) {
  hist(donnee[,i], main=colnames(donnee)[i], xlab="")
}

Pre-traimement

Donn ́ees manquantes ? Outliers

table(is.na(donnee))
## 
## FALSE 
##  1503

Aucune donnée manquante

Valeur aberrante exports max à 200 ? Bizarre Ce sont à première vue des pays riche comme malte, luxembourg, singapour import max à 174 ? Idem Finalement c’est logique Aucune valeur aberrante

Mais y a des valeurs “leviers”, certains pays comme malte, singapour se dégage des valeurs moyennes

Standardisation ?

Lorsque l’on a des données avec des unités différentes (par exemple des pourcentages, des espérances de vie, des PIB par habitant), il est recommandé de centrer et de réduire ces données. Centrer les données signifie soustraire la moyenne de la variable de toutes les observations, ce qui permet d’avoir une moyenne égale à zéro. Réduire les données signifie diviser chaque observation par l’écart-type de la variable, ce qui met toutes les variables à la même échelle. Cela facilite la comparaison entre les différentes variables et permet des analyses statistiques plus fiables. Il est cependant important de garder à l’esprit que la signification des résultats dépend toujours du contexte et de la validité des données utilisées

donnee <- data.frame(scale(donnee))

Choix des variables (regroupement ?) en vue d’une classification

Matrice de corrélation

var <- donnee[,1:9]
corrplot(cor(var), type = "upper")

La matrice de corrélation nous aide à mieux comprendre les relations entre chaque variable et pourra nous aider à interpréter plus tard.

2 - Classification des pays en utilisant les différents algorithmes abordés en cours

Utilisation des algorithmes de classification vus en cours . Ŕeflexion sur les choix op ́er ́es D ́ecider d’une classification finale . Nombre de groupes ?

Partie 1 : Algoritlme des Kmeans

Tout d’abord nous allons utiliser l’algorithme des k-means pour avoir une première idée de notre classification finale. Si on ne sait pas a priori combien de groupes comporte le jeu de donnees, on peut appliquer l’algorithme pour plusieurs choix de K possibles et tracer la courbe d’évolution de l’inertie . On lance l’algorithme des kmeans et on observe l’évolution de la variance intra-groupes en fonction du nombre de groupes. On rajoute également l’option « nstart =50 » pour stabiliser les résultats.

A la vue de ce graphique, on aurait tendance à choisir K= 3,4 ou 5 groupes en appliquant la méthode dite « du coude »

K=4
cl = kmeans(donnee,K,nstart=50)
gpe = cl$cluster
clusplot(donnee,gpe,labels=4,col.p=gpe)

La représentation en clusplot nous permet de voir qu’il y a 4 groupes qui se séparent plutôt bien sur les composante 1, 2, 3 et 4. (on le voit au travers des différents couleur sur le graphique).

Representation des groupes sur le premier plan factoriel

Partie 2 : CAH

set.seed(123)
d <- dist(donnee)
#d <- dist(e19, method = "manhattan")
#d <- dist(e19, method = "minkowski")
cah.ward <- hclust(d, method = "ward.D")
cah.min <- hclust(d, method = "single")
cah.max <- hclust(d, method = "complete")

Dengrogrammes

plot(cah.ward, hang = -1, main = "Distance de Ward", ylab = " ")

plot(cah.min, hang = -1, main = "Distance du saut minimal", ylab = " ")

plot(cah.max, hang = -1, main = "Distance du saut maximal", ylab = " ")

On s’apercoit raipdement que c’est le critère de Ward qui correspond le mieux à nos données. On voit déjà qu’on peut partitionner nos données en 3 ou 4 groupes

Fonction de perte

Pour rappel, on cherche à maximiser l’inertie inter-classe. En effet, nous avons pour objectif de créer des groupes d’individus se ressemblant fortement (inertie intra-classes faible) et tels que les groupes soient les plus distints possible (inertie inter-classes élevée). L’inertie inter-classe est logiquement maximale (égale à l’intertie totale) lorsqu’il y a autant de classes que d’individus. Nous cherchons dans le graphique ci-dessous un “coude” qui correspond à une rupture dans la courbe (moment où l’inertie inter augmente beaucoup).

plot(rev(cah.ward$height)[1:10], type = "b", main = "Distance de Ward")

plot(rev(cah.min$height)[1:10], type = "b", main = "Distance du saut minimal")

plot(rev(cah.max$height)[1:10], type = "b", main = "Distance du saut maximal")

Avec le critère de Ward, la trace de la perte d’inertie nous incite à choisir des partitions en 3 groupes (“coude” très visible).

as.matrix(donnee)
##                                enfant_mort       exports        sant.
## Afghanistan                     1.28765971 -1.1348666486  0.278251399
## Albania                        -0.53733286 -0.4782201668 -0.096725279
## Algeria                        -0.27201464 -0.0988244217 -0.963176244
## Angola                          2.00178723  0.7730561847 -1.443728879
## Antigua and Barbuda            -0.69354825  0.1601861350 -0.286033893
## Argentina                      -0.58940465 -0.8101914437  0.467560013
## Armenia                        -0.50013871 -0.7408787595 -0.879443587
## Australia                      -0.82992677 -0.7773591196  0.696914681
## Austria                        -0.84232482  0.3717722236  1.523319592
## Azerbaijan                      0.02305888  0.4812133039 -0.340642147
## Bahamas                        -0.60676192 -0.2228576461  0.391108458
## Bahrain                        -0.73570161  1.0357147775 -0.671932222
## Bangladesh                      0.27597905 -0.9159844880 -1.199812011
## Barbados                       -0.59684348 -0.0586960256  0.420232860
## Belarus                        -0.81256951  0.3754202596 -0.438937004
## Belgium                        -0.83736560  1.2874292622  1.414103084
## Belize                         -0.48278145  0.6234867083 -0.588199565
## Benin                           1.80341848 -0.6314376792 -0.988660095
## Bhutan                          0.10984521  0.0507450547 -0.588199565
## Bolivia                         0.20654998  0.0033205866 -0.719259375
## Bosnia and Herzegovina         -0.77785497 -0.4162035546  1.559725095
## Botswana                        0.35284694  0.0908734508  0.540371019
## Brazil                         -0.45798535 -1.1093303966  0.798850088
## Brunei                         -0.68858903  0.9591060212 -1.447369430
## Bulgaria                       -0.68115020  0.3316438275  0.019772330
## Burkina Faso                    1.92739895 -0.7992473357 -0.027554824
## Burundi                         1.37196643 -1.1742654376  1.741752609
## Cambodia                        0.15199858  0.4739172319 -0.413453152
## Cameroon                        1.72903019 -0.6898062554 -0.613683417
## Canada                         -0.81008990 -0.4380917707  1.632536100
## Cape Verde                     -0.29185152 -0.3067624743 -0.992300646
## Central African Republic        2.74567007 -1.0692020005 -1.032346699
## Chad                            2.77046617 -0.1571929979 -0.832116434
## Chile                          -0.73322200 -0.1243606738  0.416592310
## China                          -0.55964934 -0.5402367790 -0.635526719
## Colombia                       -0.48774067 -0.9196325240  0.281891950
## Comoros                         1.23806752 -0.8977443080 -0.839397534
## Congo Dem. Rep.                 1.92739895 -0.0003274495  0.398389558
## Congo Rep.                      0.63552242  1.6048083951 -1.585710340
## Costa Rica                     -0.69602786 -0.2885222943  1.486914090
## Cote d'Ivoire                   1.80341848  0.3462359715 -0.551794063
## Croatia                        -0.81256951 -0.1280087098  0.343781304
## Cyprus                         -0.85968208  0.3316438275 -0.307877195
## Czech Republic                 -0.86464130  0.9080335171  0.387467907
## Denmark                        -0.84728404  0.3425879355  1.668941603
## Dominican Republic             -0.09596237 -0.6715660753 -0.216863438
## Ecuador                        -0.32656605 -0.4818682028  0.452997812
## Egypt                          -0.22738167 -0.7226385795 -0.784789280
## El Salvador                    -0.47286301 -0.5183485629  0.034334531
## Equatorial Guinea               1.80341848  1.6303446471 -0.850319185
## Eritrea                         0.41979640 -1.3249293248 -1.512899335
## Estonia                        -0.83736560  1.2400047940 -0.286033893
## Fiji                           -0.35136215  0.6088945643 -0.711978275
## Finland                        -0.87455974 -0.0878803137  0.777006786
## France                         -0.84480443 -0.5219965989  1.850969117
## Gabon                           0.63056320  0.6052465282 -1.207093112
## Gambia                          1.04217837 -0.6314376792 -0.409812602
## Georgia                        -0.53981246 -0.2228576461  1.195670068
## Germany                        -0.84480443  0.0434489827  1.741752609
## Ghana                           0.90332024 -0.4234996266 -0.580918465
## Greece                         -0.85224326 -0.6934542914  1.268481073
## Grenada                        -0.58692504 -0.6314376792 -0.347923248
## Guatemala                      -0.07116628 -0.5584769590  0.012491229
## Guinea                          1.75382629 -0.3943153386 -0.686494423
## Guinea-Bissau                   1.87780676 -0.9561128841  0.613182024
## Guyana                         -0.01661487  0.3754202596 -0.522669661
## Haiti                           4.20863965 -0.9415207401  0.034334531
## Hungary                        -0.80017146  1.4844232067  0.187237642
## Iceland                        -0.88447818  0.4483809798  0.940831549
## India                           0.50906234 -0.6752141114 -1.006862847
## Indonesia                      -0.12323808 -0.6131974992 -1.531102086
## Iran                           -0.47038340 -0.6095494632 -0.442577555
## Iraq                           -0.03397213 -0.0623440616  0.580417072
## Ireland                        -0.84480443  2.2578068409  0.864379993
## Israel                         -0.83488599 -0.2228576461  0.296454151
## Italy                          -0.84976365 -0.5803651751  0.988158702
## Jamaica                        -0.50013871 -0.3578349785 -0.730181026
## Japan                          -0.86960052 -0.9524648481  0.973596501
## Jordan                         -0.42575043  0.2623311433  0.445716712
## Kazakhstan                     -0.41583199  0.1127616669 -0.919489640
## Kenya                           0.59336906 -0.7445267956 -0.752024328
## Kiribati                        0.60576711 -1.0144814603  1.632536100
## Kuwait                         -0.68115020  0.9335697692 -1.523820985
## Kyrgyz Republic                -0.21498363  0.3827163316 -0.231425639
## Lao                             1.00746384 -0.2082655020 -0.853959735
## Latvia                         -0.75553849  0.4593250878 -0.049398125
## Lebanon                        -0.69354825 -0.1936733580  0.078021134
## Lesotho                         1.52322261 -0.0623440616  1.559725095
## Liberia                         1.26534322 -0.8028953717  1.814563614
## Libya                          -0.53733286  0.8934413731 -1.068752201
## Lithuania                      -0.79769185  0.8824972650  0.081661685
## Luxembourg                     -0.87951896  4.8843927683  0.347421854
## Macedonia FYR                  -0.69106864 -0.0477519176  0.099864436
## Madagascar                      0.59336906 -0.5876612471 -1.108798254
## Malawi                          1.29509854 -0.6679180393 -0.082163078
## Malaysia                       -0.75305888  1.6704730432 -0.883084138
## Maldives                       -0.62163958  1.3312056943 -0.176817385
## Mali                            2.44811694 -0.6679180393 -0.668291671
## Malta                          -0.78033458  4.0818248460  0.667790278
## Mauritania                      1.46619159  0.3498840075 -0.875803037
## Mauritius                      -0.57700661  0.3681241876 -0.296955544
## Micronesia Fed. Sts.            0.04289576 -0.6423817873  2.688295679
## Moldova                        -0.52245520 -0.0696401337  1.778158111
## Mongolia                       -0.30176996  0.2039625671 -0.500826359
## Montenegro                     -0.78033458 -0.1498969259  0.835255591
## Morocco                        -0.11827886 -0.3250026544 -0.588199565
## Mozambique                      1.55545753 -0.3505389064 -0.584559015
## Myanmar                         0.64792047 -1.4956938904 -1.764097303
## Namibia                         0.43963327  0.2440909632 -0.012992623
## Nepal                           0.21646842 -1.1501883999 -0.569996814
## Netherlands                    -0.83736560  1.1269156777  1.850969117
## New Zealand                    -0.79521224 -0.3943153386  1.195670068
## Niger                           2.10097161 -0.6898062554 -0.602761767
## Nigeria                         2.27454427 -0.5767171391 -0.635526719
## Norway                         -0.86960052 -0.0513999536  0.969955951
## Oman                           -0.65883372  0.8970894091 -1.472853282
## Pakistan                        1.33477229 -1.0071853883 -1.680364647
## Panama                         -0.46046496  1.0539549575  0.467560013
## Paraguay                       -0.35136215  0.5103975920 -0.344282697
## Peru                           -0.44558730 -0.4855162388 -0.631886169
## Philippines                    -0.15795261 -0.2301537181 -1.167047059
## Poland                         -0.80017146 -0.0368078096  0.234564796
## Portugal                       -0.85224326 -0.4089074826  1.523319592
## Qatar                          -0.72578317  0.7730561847 -1.822346108
## Romania                        -0.66379294 -0.3104105103 -0.449858655
## Russia                         -0.70098708 -0.4344437347 -0.631886169
## Rwanda                          0.62808359 -1.0619059284  1.341292079
## Samoa                          -0.48030184 -0.4344437347 -0.125849681
## Saudi Arabia                   -0.55964934  0.3097556114 -0.919489640
## Senegal                         0.70743109 -0.5913092831 -0.420734253
## Serbia                         -0.76049771 -0.2994664023  1.304886576
## Seychelles                     -0.59188426  1.9221875279 -1.243498614
## Sierra Leone                    3.01842711 -0.8868002000  2.287835149
## Singapore                      -0.87951896  5.7964017708 -1.039627799
## Slovak Republic                -0.77537536  1.2837812262  0.718757982
## Slovenia                       -0.86960052  0.8460169049  0.944472099
## Solomon Islands                -0.25217777  0.2988115034  0.631384776
## South Africa                    0.38260226 -0.4563319507  0.773366236
## South Korea                    -0.84728404  0.3024595394  0.041615632
## Spain                          -0.85472287 -0.5694210671  0.991799253
## Sri Lanka                      -0.67123177 -0.7846551917 -1.410963927
## St. Vincent and the Grenadines -0.43566887 -0.5183485629 -0.853959735
## Sudan                           0.95291243 -0.7810071557 -0.180457935
## Suriname                       -0.35136215  0.4155486557  0.070740034
## Sweden                         -0.87455974  0.1857223871  1.024564205
## Switzerland                    -0.83736560  0.8350727969  1.705347106
## Tajikistan                      0.35036733 -0.9561128841 -0.304236644
## Tanzania                        0.83389118 -0.8174875158 -0.293314993
## Thailand                       -0.57948622  0.9262736971 -1.068752201
## Timor-Leste                     0.60328750 -1.4194134574  0.838896141
## Togo                            1.29013932 -0.0331597736  0.303735251
## Tonga                          -0.51749598 -1.0473137844 -0.635526719
## Tunisia                        -0.51749598  0.3425879355 -0.220503988
## Turkey                         -0.47534262 -0.7554709036 -0.027554824
## Turkmenistan                    0.58840984  1.2837812262 -1.571148139
## Uganda                          1.05953564 -0.8758560919  0.798850088
## Ukraine                        -0.65883372  0.2185547112  0.329219103
## United Arab Emirates           -0.73570161  1.3348537303 -1.148844307
## United Kingdom                 -0.82000833 -0.4709240948  1.028204755
## United States                  -0.76793653 -1.0473137844  4.035299280
## Uruguay                        -0.68610942 -0.5402367790  0.558573770
## Uzbekistan                     -0.04884979 -0.3432428344 -0.366125999
## Vanuatu                        -0.22490206  0.2003145311 -0.569996814
## Venezuela                      -0.52493481 -0.4599799868 -0.693775523
## Vietnam                        -0.37119902  1.1269156777  0.008850679
## Yemen                           0.44707210 -0.4052594466 -0.595480666
## Zambia                          1.11160744 -0.1498969259 -0.337001597
##                                    imports       revenu    inflation
## Afghanistan                    -0.08220771 -0.805821873  0.156864451
## Albania                         0.07062429 -0.374243349 -0.311410892
## Algeria                        -0.63983800 -0.220182266  0.786907640
## Angola                         -0.16481961 -0.583289197  1.382894441
## Antigua and Barbuda             0.49607554  0.101426731 -0.599944185
## Argentina                      -1.27594958  0.080677763  1.240992822
## Armenia                        -0.06568534 -0.541791262 -0.001119352
## Australia                      -1.07355044  1.258181668 -0.626432487
## Austria                         0.03757953  1.351552022 -0.653582997
## Azerbaijan                     -1.08181163 -0.059377768  0.569325158
## Bahamas                        -0.13177485  0.298541922 -0.773347964
## Bahrain                         0.16562797  1.242619943 -0.032337708
## Bangladesh                     -1.03637509 -0.762767766 -0.060718032
## Barbados                        0.07475488 -0.095688461 -0.705802793
## Belarus                         0.72738885 -0.049003284  0.692306561
## Belgium                         1.14870951  1.242619943 -0.558319710
## Belize                          0.43824722 -0.480581808 -0.628324509
## Benin                          -0.40026351 -0.794928665 -0.652447784
## Bhutan                          0.98348572 -0.556315539 -0.169509273
## Bolivia                        -0.52005075 -0.608706682  0.094427739
## Bosnia and Herzegovina          0.18215035 -0.385136557 -0.603728228
## Botswana                        0.18215035 -0.199433298  0.107671890
## Brazil                         -1.44943456 -0.137186396  0.059425339
## Brunei                         -0.78027822  3.291580483  0.843668288
## Bulgaria                        0.25237046 -0.095688461 -0.631162541
## Burkina Faso                   -0.71418870 -0.815158909 -0.091936388
## Burundi                        -0.31765161 -0.849705939  0.427423538
## Cambodia                        0.52085911 -0.758617972 -0.441014371
## Cameroon                       -0.82158417 -0.751355833 -0.555481677
## Canada                         -0.65636038  1.221870975 -0.464664641
## Cape Verde                      0.61586279 -0.586920266 -0.688396194
## Central African Republic       -0.84223714 -0.843273759 -0.546021570
## Chad                           -0.14003604 -0.789222699 -0.131668841
## Chile                          -0.64396859  0.116988456  0.111455933
## China                          -1.00333033 -0.394992317 -0.079638248
## Colombia                       -1.20159888 -0.323927103 -0.371009572
## Comoros                         0.19867273 -0.816196357 -0.370063562
## Congo Dem. Rep.                 0.11193024 -0.857746164  1.231532714
## Congo Rep.                      0.32259057 -0.620118614  1.222072606
## Costa Rica                     -0.49113659 -0.214995024 -0.114640647
## Cote d'Ivoire                  -0.14829723 -0.749799661 -0.226269921
## Croatia                        -0.36308815  0.153299149 -0.658502253
## Cyprus                          0.43824722  0.869138528 -0.546021570
## Czech Republic                  0.66129933  0.578652983 -0.871449283
## Denmark                        -0.13590545  1.393049957 -0.431554263
## Dominican Republic             -0.56135670 -0.313552619 -0.221539867
## Ecuador                        -0.59853205 -0.404329352 -0.029499676
## Egypt                          -0.83810654 -0.377874419  0.219301164
## El Salvador                    -0.01198760 -0.510667811 -0.485476879
## Equatorial Guinea               0.49607554  0.858764044  1.619397140
## Eritrea                        -0.97441617 -0.815677633  0.361202783
## Estonia                         0.90087383  0.288167438 -0.571563861
## Fiji                            0.70260528 -0.508074190 -0.336007173
## Finland                        -0.39200232  1.175185798 -0.702964760
## France                         -0.77614762  1.024755784 -0.636838606
## Gabon                          -1.15616234 -0.090501219  0.834208180
## Gambia                         -0.17308080 -0.803228252 -0.329385098
## Georgia                         0.24410927 -0.540235089  0.072669490
## Germany                        -0.40439410  1.206309250 -0.664462121
## Ghana                          -0.04090177 -0.730606866  0.834208180
## Greece                         -0.66875216  0.599401950 -0.672503213
## Grenada                         0.09540786 -0.308365377 -0.690761221
## Guatemala                      -0.43743886 -0.541272538 -0.249920191
## Guinea                         -0.15242782 -0.827608289  0.786907640
## Guinea-Bissau                  -0.48287540 -0.817233805 -0.455204533
## Guyana                          1.33045567 -0.586401542 -0.194105554
## Haiti                           0.73565004 -0.811527839 -0.220593856
## Hungary                         1.22306021  0.267418470 -0.515749224
## Iceland                        -0.14829723  1.123313380 -0.218701835
## India                          -0.81745357 -0.660579101  0.113347954
## Indonesia                      -1.01159152 -0.452051977  0.711226777
## Iran                           -1.13550936  0.013243619  0.767987425
## Iraq                           -0.52831194 -0.230556749  0.834208180
## Ireland                         1.63611968  1.481233069 -1.040785215
## Israel                         -0.57787908  0.646087127 -0.568725829
## Italy                          -0.81332298  0.988445091 -0.705991995
## Jamaica                         0.11193024 -0.474357117  0.191866850
## Japan                          -1.37508386  0.967696123 -0.915911790
## Jordan                          0.91326561 -0.398104662  0.061317361
## Kazakhstan                     -0.70179692  0.153299149  1.108551311
## Kenya                          -0.54896492 -0.760692869 -0.538453483
## Kiribati                        1.36350043 -0.799597183 -0.592376098
## Kuwait                         -0.68114395  3.011469422  0.323362351
## Kyrgyz Republic                 1.43785114 -0.744612419  0.209841056
## Lao                             0.09953845 -0.682884241  0.134160192
## Latvia                          0.33911295  0.059928796 -0.812985816
## Lebanon                         0.54977328 -0.043816042 -0.713654682
## Lesotho                         2.23505591 -0.765880111 -0.343575259
## Liberia                         1.88808596 -0.853025774 -0.218701835
## Libya                          -0.19786437  0.646087127  0.607165589
## Lithuania                       0.83891490  0.205171568 -0.511019170
## Luxembourg                      3.92859974  3.867364331 -0.393713832
## Macedonia FYR                   0.46303079 -0.297990894 -0.543183537
## Madagascar                     -0.16068901 -0.817233805  0.095373749
## Malawi                         -0.49526718 -0.835907876  0.408503322
## Malaysia                        0.99587750  0.205171568 -0.048419891
## Maldives                        0.76456420 -0.344676071 -0.463718630
## Mali                           -0.48700600 -0.792335044 -0.322763022
## Malta                           4.42427111  0.578652983 -0.373847605
## Mauritania                      0.59107922 -0.717120037  1.051790663
## Mauritius                       0.63238517 -0.064565009 -0.629270519
## Micronesia Fed. Sts.            1.40893697 -0.716082589 -0.376685637
## Moldova                         1.30567211 -0.686515310  0.313902243
## Mongolia                        0.40520246 -0.489400119  2.972192577
## Montenegro                      0.65303814 -0.163122605 -0.584808012
## Morocco                        -0.16068901 -0.555278091 -0.643839086
## Mozambique                     -0.02850998 -0.841717587 -0.013417492
## Myanmar                        -1.93412267 -0.696371070 -0.070178140
## Namibia                         0.57042625 -0.450495805 -0.399389896
## Nepal                          -0.43330826 -0.786110354  0.692306561
## Netherlands                     0.69021350  1.470858585 -0.655948024
## New Zealand                    -0.78027822  0.786142658 -0.383307713
## Niger                           0.09127726 -0.847112318 -0.494936987
## Nigeria                        -1.21812126 -0.622193511  9.102342527
## Norway                         -0.75962525  2.342315220 -0.173293316
## Oman                           -0.23503972  1.460484101  0.739607101
## Pakistan                       -1.13550936 -0.667322515  0.294982027
## Panama                          1.29328032 -0.090501219 -0.491152943
## Paraguay                        0.19041154 -0.511186535 -0.159103154
## Peru                           -0.95376320 -0.372687177 -0.195997575
## Philippines                    -0.42504707 -0.598850922 -0.336953184
## Poland                         -0.19786437  0.241482261 -0.579131947
## Portugal                       -0.39200232  0.521593322 -0.675341245
## Qatar                          -0.95376320  5.594715874 -0.075854204
## Romania                        -0.33417399  0.033992586 -0.402227929
## Russia                         -1.06528925  0.308916405  0.607165589
## Rwanda                         -0.69766632 -0.819308702 -0.489260922
## Samoa                           0.25650105 -0.609225406 -0.573455883
## Saudi Arabia                   -0.57374848  1.465671343  0.890968828
## Senegal                        -0.27221507 -0.776254594 -0.561157742
## Serbia                          0.04171013 -0.230556749 -0.179915392
## Seychelles                      2.52419754  0.168860875 -1.134440284
## Sierra Leone                   -0.51178956 -0.826052116  0.890968828
## Singapore                       5.25039005  2.850664923 -0.740521389
## Slovak Republic                 1.27675794  0.417848485 -0.690288216
## Slovenia                        0.66129933  0.599401950 -0.829541005
## Solomon Islands                 1.41719816 -0.797003562 -0.091936388
## South Africa                   -0.80506179 -0.266867442 -0.135452885
## South Korea                    -0.02850998  0.687585062 -0.437230328
## Spain                          -0.82984536  0.796517142 -0.721033567
## Sri Lanka                      -0.82984536 -0.445308563  1.420734873
## St. Vincent and the Grenadines  0.42172484 -0.374762073 -0.316140946
## Sudan                          -1.22638245 -0.714526416  1.118011419
## Suriname                       -0.35069637 -0.152748121 -0.055041967
## Sweden                         -0.25569269  1.335990296 -0.642420070
## Switzerland                     0.26476224  1.989582772 -0.706181197
## Tajikistan                      0.48368376 -0.779885664  0.446343754
## Tanzania                       -0.73484168 -0.780923112  0.138890246
## Thailand                        0.57455684 -0.189058814 -0.350197335
## Timor-Leste                    -0.78853941 -0.793372493  1.770758867
## Togo                            0.42998603 -0.826570841 -0.624540466
## Tonga                           0.55390387 -0.631011822 -0.388037767
## Tunisia                         0.34737414 -0.349863312 -0.374793616
## Turkey                         -0.88354309  0.044367070 -0.073016172
## Turkmenistan                   -0.09873009 -0.373724625 -0.517641246
## Uganda                         -0.75549465 -0.809452942  0.266601703
## Ukraine                         0.17388916 -0.483694153  0.531484726
## United Arab Emirates            0.69021350  2.098514852  0.446343754
## United Kingdom                 -0.66462157  0.988445091 -0.587646045
## United States                  -1.28421077  1.673161018 -0.620756422
## Uruguay                        -0.88767368 -0.002318107 -0.271678439
## Uzbekistan                     -0.75962525 -0.669397412  0.824748072
## Vanuatu                         0.23997867 -0.736312832 -0.488314911
## Venezuela                      -1.20986007 -0.033441558  3.606019809
## Vietnam                         1.37589222 -0.656429307  0.408503322
## Yemen                          -0.51592016 -0.656948031  1.496415737
## Zambia                         -0.66049097 -0.719194934  0.588245374
##                                   esper_vie         fert        pib_h
## Afghanistan                    -1.614237166  1.897176463 -0.677143083
## Albania                         0.645923798 -0.857394179 -0.484167091
## Algeria                         0.668412962 -0.038289240 -0.463980176
## Angola                         -1.175698472  2.121769753 -0.514720259
## Antigua and Barbuda             0.702146708 -0.540321300 -0.041691745
## Argentina                       0.589700889 -0.381784860 -0.145354280
## Armenia                         0.308586341 -0.830971439 -0.531633620
## Australia                       1.286864967 -0.672434999  2.124309640
## Austria                         1.118196239 -0.996113564  1.851513496
## Azerbaijan                     -0.163686100 -0.679040684 -0.388688441
## Bahamas                         0.364809250 -0.718674794  0.820344071
## Bahrain                         0.612190052 -0.520504245  0.422061700
## Bangladesh                     -0.017506535 -0.408207600 -0.665958441
## Barbados                        0.690902126 -0.771520274  0.165633325
## Belarus                        -0.017506535 -0.963085139 -0.378322187
## Belgium                         1.061973329 -0.718674794  1.715115424
## Belize                          0.094939284 -0.157191570 -0.470527284
## Benin                          -0.984540579  1.593314954 -0.665958441
## Bhutan                          0.173651358 -0.375179175 -0.588375218
## Bolivia                         0.117428448  0.166486995 -0.599287064
## Bosnia and Herzegovina          0.702146708 -1.081987469 -0.455796292
## Botswana                       -1.513035929 -0.044894925 -0.360863234
## Brazil                          0.409787578 -0.758308904 -0.096250974
## Brunei                          0.735880453 -0.731886164  1.218626441
## Bulgaria                        0.376053832 -0.910239659 -0.334129212
## Burkina Faso                   -1.423079274  1.930204888 -0.675942780
## Burundi                        -1.445568438  2.187826603 -0.694711155
## Cambodia                       -0.501023557 -0.044894925 -0.664430783
## Cameroon                       -1.490546765  1.428172829 -0.635841747
## Canada                          1.208152894 -0.870605549  1.878793110
## Cape Verde                      0.218629685 -0.183614310 -0.526723289
## Central African Republic       -2.592515793  1.494229679 -0.682980921
## Chad                           -1.580503421  2.405814208 -0.658374709
## Chile                           0.960772092 -0.705463424 -0.003500285
## China                           0.454765906 -0.897028289 -0.458524253
## Colombia                        0.657168380 -0.619589519 -0.366319157
## Comoros                        -0.523512721  1.190368169 -0.665358290
## Congo Dem. Rep.                -1.468057602  2.372785783 -0.689091555
## Congo Rep.                     -1.141964726  1.322481869 -0.557822050
## Costa Rica                      1.106951657 -0.679040684 -0.259928660
## Cote d'Ivoire                  -1.602992585  1.533863789 -0.640752078
## Croatia                         0.645923798 -0.923451029  0.029235252
## Cyprus                          1.050728747 -1.009324934  0.973109911
## Czech Republic                  0.780858781 -0.949873769  0.372958394
## Denmark                         1.005750419 -0.712069109  2.457120936
## Dominican Republic              0.454765906 -0.229854105 -0.409966540
## Ecuador                         0.690902126 -0.190219995 -0.453068331
## Egypt                          -0.006261953  0.159881310 -0.565460342
## El Salvador                     0.398542996 -0.447841710 -0.544182243
## Equatorial Guinea              -1.085741816  1.494229679  0.225648476
## Eritrea                        -0.995785161  1.097888579 -0.681016789
## Estonia                         0.612190052 -0.811154384  0.089250404
## Fiji                           -0.590980212 -0.183614310 -0.508173152
## Finland                         1.061973329 -0.712069109  1.813322035
## France                          1.219397476 -0.606378149  1.507790354
## Gabon                          -0.860850178  0.747787274 -0.229921085
## Gambia                         -0.568491048  1.824513928 -0.676652050
## Georgia                         0.252363431 -0.679040684 -0.545819020
## Germany                         1.073217911 -1.029141989  1.573261429
## Ghana                          -0.939562252  0.873295289 -0.635841747
## Greece                          1.106951657 -0.969690824  0.760328919
## Grenada                         0.083694703 -0.467658765 -0.305212820
## Guatemala                       0.083694703  0.285389325 -0.552911719
## Guinea                         -1.411834692  1.580103584 -0.671959957
## Guinea-Bissau                  -1.681704658  1.388538719 -0.677470439
## Guyana                         -0.568491048 -0.196825680 -0.541454281
## Haiti                          -4.324181408  0.252360900 -0.671196127
## Hungary                         0.443521324 -1.121621579  0.007411561
## Iceland                         1.286864967 -0.494081505  1.578717351
## India                          -0.489778975 -0.229854105 -0.633659378
## Indonesia                      -0.073729444 -0.309122325 -0.537635135
## Iran                            0.443521324 -0.784731644 -0.351042573
## Iraq                           -0.377333156  1.064860154 -0.461797807
## Ireland                         1.106951657 -0.593166779  1.949720108
## Israel                          1.219397476  0.054190350  0.962198066
## Italy                           1.253131222 -0.982902194  1.245906056
## Jamaica                         0.466010488 -0.513898560 -0.451977146
## Japan                           1.376821623 -1.029141989  1.720571346
## Jordan                          0.589700889  0.470348505 -0.506536375
## Kazakhstan                     -0.242398173 -0.229854105 -0.212462131
## Kenya                          -0.872094760  0.939352139 -0.654555563
## Kiribati                       -1.108230980  0.589250834 -0.626021086
## Kuwait                          0.859570855 -0.487475820  1.393215973
## Kyrgyz Republic                -0.231153591  0.100430145 -0.659302216
## Lao                            -0.759648941  0.133458570 -0.645116816
## Latvia                          0.286097177 -1.048959044 -0.090795051
## Lebanon                         1.039484165 -0.883816919 -0.223919569
## Lesotho                        -2.704961612  0.232543845 -0.643480039
## Liberia                        -1.096986398  1.368721664 -0.689473469
## Libya                           0.623434634 -0.355362120 -0.047147668
## Lithuania                       0.297341759 -0.956479454 -0.052603591
## Luxembourg                      1.208152894 -0.870605549  5.021404691
## Macedonia FYR                   0.387298414 -0.976296509 -0.459615438
## Madagascar                     -1.096986398  1.091282894 -0.684781375
## Malawi                         -1.962819206  1.560286529 -0.682271651
## Malaysia                        0.443521324 -0.527109930 -0.212462131
## Maldives                        0.825837109 -0.474264450 -0.319943812
## Mali                           -1.243165963  2.379391468 -0.668686403
## Malta                           1.095707075 -1.048959044  0.443885392
## Mauritania                     -0.264887337  1.342298924 -0.641843262
## Mauritius                       0.319830923 -0.910239659 -0.270840506
## Micronesia Fed. Sts.           -0.579735630  0.338234805 -0.551274942
## Moldova                        -0.096218608 -1.108410209 -0.618382794
## Mongolia                       -0.489778975 -0.203431365 -0.562732381
## Montenegro                      0.657168380 -0.778125959 -0.342858688
## Morocco                         0.331075505 -0.243065475 -0.552911719
## Mozambique                     -1.805395059  1.725428653 -0.684454020
## Myanmar                        -0.422311484 -0.355362120 -0.653409819
## Namibia                        -1.344367201  0.430714395 -0.424151939
## Nepal                          -0.253642755 -0.223248420 -0.675015273
## Netherlands                     1.140685402 -0.764914589  2.037014874
## New Zealand                     1.163174566 -0.513898560  1.131331675
## Niger                          -1.321878037  3.000325857 -0.688327725
## Nigeria                        -1.130720144  1.910387833 -0.580191334
## Norway                          1.174419148 -0.659223629  4.082985955
## Oman                            0.623434634 -0.031683555  0.345678780
## Pakistan                       -0.590980212  0.595856519 -0.650572739
## Panama                          0.814592527 -0.216642735 -0.266475768
## Paraguay                        0.398542996 -0.143980200 -0.531088028
## Peru                            0.825837109 -0.269488215 -0.433427008
## Philippines                    -0.174930682  0.140064255 -0.591103180
## Poland                          0.645923798 -1.015930619 -0.019868054
## Portugal                        1.039484165 -1.029141989  0.520268312
## Qatar                           1.005750419 -0.579955409  3.128199451
## Romania                         0.353564668 -0.897028289 -0.258291884
## Russia                         -0.152441518 -0.910239659 -0.123530588
## Rwanda                         -0.669692286  1.031831729 -0.676597491
## Samoa                           0.106183866  0.919535084 -0.519084997
## Saudi Arabia                    0.510988815  0.007950555  0.345678780
## Senegal                        -0.737159777  1.395144404 -0.652755108
## Serbia                          0.466010488 -1.022536304 -0.412148909
## Seychelles                      0.319830923 -0.513898560 -0.118074665
## Sierra Leone                   -1.749172149  1.487623994 -0.685545205
## Singapore                       1.365577041 -1.187678429  1.835145727
## Slovak Republic                 0.555967143 -1.002719249  0.198368862
## Slovenia                        1.005750419 -0.910239659  0.569371618
## Solomon Islands                -0.995785161  0.853478234 -0.636932932
## South Africa                   -1.827884223 -0.236459790 -0.310123151
## South Korea                     1.073217911 -1.134832949  0.498444620
## Spain                           1.275620385 -1.042353359  0.967653988
## Sri Lanka                       0.432276742 -0.494081505 -0.554002904
## St. Vincent and the Grenadines  0.117428448 -0.579955409 -0.367410341
## Sudan                          -0.478534393  1.276242074 -0.626566678
## Suriname                       -0.028751117 -0.282699585 -0.254472738
## Sweden                          1.230642058 -0.639406574  2.135221486
## Switzerland                     1.309354131 -0.943268084  3.362804135
## Tajikistan                     -0.107463190  0.371263230 -0.667049626
## Tanzania                       -1.265655127  1.639554749 -0.669013758
## Thailand                        0.679657544 -0.923451029 -0.430153454
## Timor-Leste                     0.061205539  2.168009548 -0.510901113
## Togo                           -1.333122619  1.269636389 -0.680689433
## Tonga                          -0.073729444  0.635490629 -0.513629075
## Tunisia                         0.713391290 -0.533715615 -0.481439130
## Turkey                          0.859570855 -0.527109930 -0.123530588
## Turkmenistan                   -0.298621083 -0.077923350 -0.465071361
## Uganda                         -1.546769675  2.115164068 -0.674851596
## Ukraine                        -0.017506535 -0.996113564 -0.545273427
## United Arab Emirates            0.668412962 -0.712069109  1.202258672
## United Kingdom                  1.095707075 -0.679040684  1.415039665
## United States                   0.915793764 -0.672434999  1.933352339
## Uruguay                         0.657168380 -0.573349724 -0.058059514
## Uzbekistan                     -0.197419845 -0.401601915 -0.632022601
## Vanuatu                        -0.849605596  0.364657545 -0.545273427
## Venezuela                       0.544722561 -0.315728010  0.029235252
## Vietnam                         0.286097177 -0.659223629 -0.635841747
## Yemen                          -0.343599410  1.137522689 -0.635841747
## Zambia                         -2.086509607  1.619737694 -0.627657863
NbClust(as.matrix(donnee), min.nc = 3, max.nc = 15, method = "ward.D")

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 4 proposed 3 as the best number of clusters 
## * 9 proposed 4 as the best number of clusters 
## * 1 proposed 5 as the best number of clusters 
## * 1 proposed 8 as the best number of clusters 
## * 5 proposed 9 as the best number of clusters 
## * 1 proposed 12 as the best number of clusters 
## * 1 proposed 14 as the best number of clusters 
## * 1 proposed 15 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  4 
##  
##  
## *******************************************************************
## $All.index
##        KL      CH Hartigan     CCC     Scott      Marriot    TrCovW   TraceW
## 3  1.8427 57.8307  20.9221 -2.4313  418.9626 5.164539e+16 17615.022 876.1166
## 4  1.5564 50.1387  14.8863 -2.6786  609.3518 2.936225e+16 13591.412 776.9927
## 5  1.1442 44.4853  12.5772 -3.1997  758.7814 1.875028e+16 12060.060 711.9705
## 6  0.2926 40.6143  28.1333 -3.4454  808.6017 2.003593e+16  9447.050 660.6776
## 7  2.0767 44.1722  16.2945  0.1436  962.9977 1.081897e+16  6363.185 562.4029
## 8  0.5419 43.7703  28.2797  1.4605 1070.1097 7.440776e+15  4995.833 510.4213
## 9  4.3721 48.3399   9.3875  5.1119 1220.3724 3.829616e+15  3394.298 433.3464
## 10 1.1997 46.2701   8.1650  5.2609 1293.2347 3.056237e+15  3031.433 409.0434
## 11 0.8340 44.3410   8.9717  5.3083 1376.7840 2.242316e+15  2823.262 388.8221
## 12 1.2044 43.1654   7.8186  5.6184 1447.0356 1.752186e+15  2505.380 367.6767
## 13 0.9742 41.9434   7.8612  5.7962 1506.8698 1.437148e+15  2361.741 350.0208
## 14 1.5395 41.0299   5.8597  6.0549 1560.7539 1.207096e+15  2068.108 333.0212
## 15 1.2204 39.7156   5.0920  6.0050 1614.6635 1.003397e+15  1975.666 320.7374
##    Friedman  Rubin Cindex     DB Silhouette   Duda Pseudot2   Beale Ratkowsky
## 3   25.3844 1.7053 0.2347 1.5929     0.2289 0.6755  15.3735  2.7975    0.3307
## 4   36.3323 1.9228 0.2246 1.4508     0.2470 0.8298  12.9207  1.2123    0.3286
## 5   40.4147 2.0984 0.2063 1.7295     0.2079 0.7280  24.6545  2.2097    0.3070
## 6   42.7143 2.2613 0.2032 1.7717     0.1599 0.3414  17.3592 10.4241    0.2951
## 7   51.2007 2.6565 0.1987 1.5066     0.1827 0.7968  10.4568  1.4951    0.2928
## 8   54.2108 2.9270 0.1882 1.4706     0.2036 1.0665  -1.6830 -0.3609    0.2832
## 9   56.8841 3.4476 0.3108 1.2326     0.2160 0.7129  10.4715  2.3289    0.2800
## 10  59.8853 3.6524 0.2997 1.2020     0.2206 0.7251  12.1343  2.2081    0.2688
## 11  62.3662 3.8424 0.2914 1.2141     0.2056 0.4977  12.1126  5.5951    0.2587
## 12  64.6251 4.0634 0.2862 1.1860     0.2105 0.6908   9.4000  2.5657    0.2503
## 13  68.3495 4.2683 0.2798 1.2286     0.1915 0.7334  11.6328  2.1168    0.2424
## 14  70.8060 4.4862 0.2721 1.2700     0.1875 0.7291   7.4314  2.1250    0.2353
## 15  72.5606 4.6580 0.2654 1.3223     0.1767 0.5385  13.7138  4.8442    0.2286
##        Ball Ptbiserial    Frey McClain   Dunn Hubert SDindex Dindex   SDbw
## 3  292.0389     0.4053 -0.1502  1.1448 0.0751 0.0014  2.8973 1.9790 0.9576
## 4  194.2482     0.4357  0.4909  1.1797 0.0757 0.0016  3.0800 1.8707 1.0002
## 5  142.3941     0.4312  5.5517  1.5461 0.0757 0.0019  3.1602 1.7666 0.9660
## 6  110.1129     0.3474 -0.1479  2.5747 0.0685 0.0019  3.1581 1.6756 0.7597
## 7   80.3433     0.3571  0.1256  2.5488 0.0685 0.0022  3.1016 1.5843 0.6454
## 8   63.8027     0.3659 -0.1291  2.8953 0.0717 0.0023  3.1233 1.5211 0.6410
## 9   48.1496     0.3835  0.1872  2.8069 0.1221 0.0025  2.9451 1.4625 0.4967
## 10  40.9043     0.3829  0.8481  2.9427 0.1221 0.0026  2.9247 1.4258 0.4672
## 11  35.3475     0.3608  0.0927  3.4443 0.1221 0.0026  3.1190 1.3866 0.4425
## 12  30.6397     0.3617  0.4867  3.4868 0.1221 0.0026  3.0365 1.3450 0.4064
## 13  26.9247     0.3521  1.0162  3.7714 0.1154 0.0027  2.9761 1.3048 0.3864
## 14  23.7872     0.3208  0.4286  4.6963 0.1154 0.0027  3.4028 1.2676 0.3676
## 15  21.3825     0.3095  1.4422  5.1586 0.1154 0.0028  3.4239 1.2396 0.3519
## 
## $All.CriticalValues
##    CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 3          0.6825            14.8875       0.0037
## 4          0.7508            20.9124       0.2845
## 5          0.7548            21.4445       0.0200
## 6          0.4954             9.1671       0.0000
## 7          0.7098            16.7607       0.1478
## 8          0.6621            13.7821       1.0000
## 9          0.6573            13.5542       0.0158
## 10         0.6825            14.8875       0.0216
## 11         0.5447            10.0311       0.0000
## 12         0.6292            12.3746       0.0083
## 13         0.6825            14.8875       0.0282
## 14         0.6225            12.1297       0.0296
## 15         0.5901            11.1141       0.0000
## 
## $Best.nc
##                     KL      CH Hartigan     CCC    Scott      Marriot  TrCovW
## Number_clusters 9.0000  3.0000   9.0000 14.0000   4.0000 5.000000e+00    4.00
## Value_Index     4.3721 57.8307  18.8923  6.0549 190.3892 1.189761e+16 4023.61
##                  TraceW Friedman   Rubin Cindex     DB Silhouette   Duda
## Number_clusters  9.0000    4.000  9.0000 8.0000 12.000      4.000 4.0000
## Value_Index     52.7719   10.948 -0.3158 0.1882  1.186      0.247 0.8298
##                 PseudoT2  Beale Ratkowsky    Ball PtBiserial Frey McClain
## Number_clusters   4.0000 4.0000    3.0000  4.0000     4.0000    2  3.0000
## Value_Index      12.9207 1.2123    0.3307 97.7907     0.4357   NA  1.1448
##                   Dunn Hubert SDindex Dindex    SDbw
## Number_clusters 9.0000      0  3.0000      0 15.0000
## Value_Index     0.1221      0  2.8973      0  0.3519
## 
## $Best.partition
##                    Afghanistan                        Albania 
##                              1                              2 
##                        Algeria                         Angola 
##                              2                              1 
##            Antigua and Barbuda                      Argentina 
##                              2                              2 
##                        Armenia                      Australia 
##                              2                              3 
##                        Austria                     Azerbaijan 
##                              3                              2 
##                        Bahamas                        Bahrain 
##                              2                              4 
##                     Bangladesh                       Barbados 
##                              1                              2 
##                        Belarus                        Belgium 
##                              2                              3 
##                         Belize                          Benin 
##                              2                              1 
##                         Bhutan                        Bolivia 
##                              1                              1 
##         Bosnia and Herzegovina                       Botswana 
##                              2                              1 
##                         Brazil                         Brunei 
##                              2                              4 
##                       Bulgaria                   Burkina Faso 
##                              2                              1 
##                        Burundi                       Cambodia 
##                              1                              1 
##                       Cameroon                         Canada 
##                              1                              3 
##                     Cape Verde       Central African Republic 
##                              2                              1 
##                           Chad                          Chile 
##                              1                              2 
##                          China                       Colombia 
##                              2                              2 
##                        Comoros                Congo Dem. Rep. 
##                              1                              1 
##                     Congo Rep.                     Costa Rica 
##                              1                              2 
##                  Cote d'Ivoire                        Croatia 
##                              1                              2 
##                         Cyprus                 Czech Republic 
##                              2                              2 
##                        Denmark             Dominican Republic 
##                              3                              2 
##                        Ecuador                          Egypt 
##                              2                              1 
##                    El Salvador              Equatorial Guinea 
##                              2                              1 
##                        Eritrea                        Estonia 
##                              1                              2 
##                           Fiji                        Finland 
##                              1                              3 
##                         France                          Gabon 
##                              3                              1 
##                         Gambia                        Georgia 
##                              1                              2 
##                        Germany                          Ghana 
##                              3                              1 
##                         Greece                        Grenada 
##                              3                              2 
##                      Guatemala                         Guinea 
##                              2                              1 
##                  Guinea-Bissau                         Guyana 
##                              1                              1 
##                          Haiti                        Hungary 
##                              1                              2 
##                        Iceland                          India 
##                              3                              1 
##                      Indonesia                           Iran 
##                              2                              2 
##                           Iraq                        Ireland 
##                              1                              3 
##                         Israel                          Italy 
##                              3                              3 
##                        Jamaica                          Japan 
##                              2                              3 
##                         Jordan                     Kazakhstan 
##                              2                              2 
##                          Kenya                       Kiribati 
##                              1                              1 
##                         Kuwait                Kyrgyz Republic 
##                              4                              1 
##                            Lao                         Latvia 
##                              1                              2 
##                        Lebanon                        Lesotho 
##                              2                              1 
##                        Liberia                          Libya 
##                              1                              4 
##                      Lithuania                     Luxembourg 
##                              2                              4 
##                  Macedonia FYR                     Madagascar 
##                              2                              1 
##                         Malawi                       Malaysia 
##                              1                              2 
##                       Maldives                           Mali 
##                              2                              1 
##                          Malta                     Mauritania 
##                              4                              1 
##                      Mauritius           Micronesia Fed. Sts. 
##                              2                              1 
##                        Moldova                       Mongolia 
##                              2                              2 
##                     Montenegro                        Morocco 
##                              2                              2 
##                     Mozambique                        Myanmar 
##                              1                              1 
##                        Namibia                          Nepal 
##                              1                              1 
##                    Netherlands                    New Zealand 
##                              3                              3 
##                          Niger                        Nigeria 
##                              1                              1 
##                         Norway                           Oman 
##                              3                              4 
##                       Pakistan                         Panama 
##                              1                              2 
##                       Paraguay                           Peru 
##                              2                              2 
##                    Philippines                         Poland 
##                              1                              2 
##                       Portugal                          Qatar 
##                              3                              4 
##                        Romania                         Russia 
##                              2                              2 
##                         Rwanda                          Samoa 
##                              1                              2 
##                   Saudi Arabia                        Senegal 
##                              4                              1 
##                         Serbia                     Seychelles 
##                              2                              2 
##                   Sierra Leone                      Singapore 
##                              1                              4 
##                Slovak Republic                       Slovenia 
##                              2                              2 
##                Solomon Islands                   South Africa 
##                              1                              1 
##                    South Korea                          Spain 
##                              2                              3 
##                      Sri Lanka St. Vincent and the Grenadines 
##                              2                              2 
##                          Sudan                       Suriname 
##                              1                              2 
##                         Sweden                    Switzerland 
##                              3                              3 
##                     Tajikistan                       Tanzania 
##                              1                              1 
##                       Thailand                    Timor-Leste 
##                              2                              1 
##                           Togo                          Tonga 
##                              1                              2 
##                        Tunisia                         Turkey 
##                              2                              2 
##                   Turkmenistan                         Uganda 
##                              1                              1 
##                        Ukraine           United Arab Emirates 
##                              2                              4 
##                 United Kingdom                  United States 
##                              3                              3 
##                        Uruguay                     Uzbekistan 
##                              2                              1 
##                        Vanuatu                      Venezuela 
##                              1                              2 
##                        Vietnam                          Yemen 
##                              2                              1 
##                         Zambia 
##                              1

Nbclust Cutree

nbc <- 3
gpe.ward <- cutree(cah.ward, k = nbc) # Classe affectée pour chaque individu
gpe.min <- cutree(cah.min, k = nbc)
gpe.max <- cutree(cah.max, k = nbc)
plot(cah.ward, hang = -1, main = "Distance de Ward")
rect.hclust(cah.ward, nbc, border = "blue")

plot(cah.min, hang = -1, main = "Distance du saut minimal")
rect.hclust(cah.min, nbc, border = "blue")

plot(cah.max, hang = -1, main = "Distance du saut maximal")
rect.hclust(cah.max, nbc, border = "blue")

faire une clusplot

clusplot(donnee, gpe.ward, labels = nbc, col.p = as.numeric(gpe.ward))

Partie 3 : Agragation autour des centres mobiles

Classifiaction mixte Classifiaction finale

3 - Comparaison des résultats obtenus avec les différentes méthodes

Caract ́erisation de la partition obtenue Repr ́esentation informative des r ́esultats . Graphiques adapt ́es, repr ́esentations factorielles si adapt ́ees Optionnel : Repr ́esentation spatiale des r ́esultats sur la carte de Rennes Faire une ACP

4 - Conclusion vis à vis des choix effectués

Quels points peuvent ˆetre critiqu ́es dans vos choix Quelles pistes pourraient ˆetre explor ́ees pour aller plus loin et/ou mieux explorer ces donn ́ees ?

5 - Suggestion d’une liste de pays à aider en priorité